Finding the dimensions of a rectangular box

In summary, the conversation revolves around finding the dimensions of a rectangular box with a volume of 144 cubic inches and a base that is twice as wide as it is deep. The bottom of the box must be made of a stronger and more expensive material, while the sides and top can be made of a cheaper material. The goal is to minimize the cost, which requires an equation for both the volume and the surface area of the box.
  • #1
hellomaxwalke
1
0
I'm worried about the process of solving this problem, can anyone help me?

We are to make a rectangular box, including the top, that has a volume of 144 cubic inches and for which the base is twice as wide as it is deep. The bottom, which must be strong, is made of a material that is three times as expensive as that used for the sides and the top. Find the dimensions of the box that minimize its cost.

I know I must have two equations with two variables in total but I'm not sure what to do after that. Maybe 144=(2x)(x)(y)? and another

Thanks to anyone who can shed some light on this for me, I've been trying for a bit but not sure where to start.
 
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  • #2
You wrote down an equation for the volume of the box. If you want to minimize the cost, you also need an equation for the cost. That will depend on the amount of material you need, in other words the surface area of the box.
 

Related to Finding the dimensions of a rectangular box

What is the formula for finding the dimensions of a rectangular box?

The formula for finding the dimensions of a rectangular box is length x width x height, where length is the longest side, width is the shorter side, and height is the distance from the base to the top of the box.

How do I measure the length, width, and height of a rectangular box?

You can measure the length, width, and height of a rectangular box using a ruler or measuring tape. Measure the longest side for the length, the shorter side for the width, and the distance from the base to the top for the height.

What units should I use to measure the dimensions of a rectangular box?

The units you use to measure the dimensions of a rectangular box will depend on the size of the box. For smaller boxes, you can use centimeters or inches. For larger boxes, you may need to use meters or feet.

What if my rectangular box has irregular dimensions?

If your rectangular box has irregular dimensions, you can still use the same formula to find the dimensions. However, you may need to measure each side separately and then add them together to find the total length, width, and height of the box.

Can I find the dimensions of a rectangular box if I only know its volume?

Yes, you can find the dimensions of a rectangular box if you know its volume. The formula for volume is length x width x height, so if you know the volume and two of the dimensions, you can solve for the third dimension.

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